Thank you for the support. I just found out what was the problem - it was a graphic card driver.
The log looked like this:
Spine Launcher 3.5.51
Windows 10 Home x86 6.2
Java 1.7.0_80 Esoteric Software
32-bit Server VM
Up to date: Spine 3.5.51
Spine 3.5.51 Professional
Licensed to: #############
NVIDIA Corporation
GeForce GTX 650/PCIe/SSE2
4.5.0 NVIDIA 382.33
Started.
The same way it looks if everything is ok. After lots of unsuccessful attempts to find out what the problem is, I checked the Windows event log and Bingo!
The NVIDIA OpenGL driver has encountered
an out of memory error. This application might
behave inconsistently and fail.
And after that crash happened inside of nvoglv32.DLL.
Driver update helped and now the editor works again. It would be great if you were able to detect such situations and write something to the log.